Tuesday, January 25, 2011
A Sidewalk Feature Takes Me Back
If we look at it from further out, we realize that it's really a wheelchair-ramp to an unmarked blue-green door of the Fire Department.
I was caught up with the idea that I had a trajectory. As a body in motion I leave a track. If I pass through an opening, and then later, upon return, choose not to pass through that opening in the reverse direction, then I have wound my trajectory around one side of that opening. In the case of the wheel-chair ramp, if I take the high side going east, and take the low side coming back west, altogether I will have wound my trajectory once counter-clockwise around the railing.
Imagine I was leaving a string behind me, everywhere. One long, long, string, like the drag line of spider, all the way back to the hospital room in Greenville General where I was born, where it would be anchored. Every time I were to wind it around an obstacle, it would be that much harder to pull the string straight, if I ever wanted to.
That's exactly what I imagined when I was 6 or 7, and it horrified me then, that I might be in that fix. Not to be able to straighten out my life path! It would be like being caught in a trap, ready to be devoured by some monster. I wouldn't be able to run freely, my string radiating freely, pivoting around South Carolina.
Fifteen years later I was an undergraduate discovering my own personal proof of the Fundamental Theorem of Algebra (which says that complex polynomials factor completely) and my proof ended up being the winding number proof. It's an approach that derives the theorem by studying the way polynomials map circles in the complex plane to curves, with particular attention to the number of times the curves wind around zero. Discovering that proof drew me further into the mathematics of properties of space that stay the same when you straighten wrinkles, and so I ended up being a topologist. But my original fascination with the subject was rooted in fear of being trapped in a tangle.
I'm now utterly over that childhood fear. I still imagine the drag line behind my life trajectory. The difference is now I love the tangles. Now I deliberately wind myself around things. If you see me walking down the street and I weave first right then left around various sidewalk signs, light posts, and such, you'll know that's what I'm doing. I'm tangling myself in everything, because I've figured out who the monster is, and I'm quite happy with being devoured by her.